Optical property modeling method and device, optical parameter measurement method

Abstract

The present invention provides an optical property modeling method and device, and an optical parameter measurement method, wherein the optical property modeling method comprises: obtaining characteristic parameters of a periodic medium, and constructing a first coupled wave equation group based on the characteristic parameters and a strict coupled wave analysis method; the periodic medium is symmetrical about the incident plane of the light beam; obtaining a linear combination of two orthogonal components of an electric field or two orthogonal components of a magnetic field, and constructing a second coupled wave equation group based on the first coupled wave equation group and a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field; simplifying the second coupled wave equation group according to the symmetry of the periodic medium; solving the simplified second coupled wave equation group to obtain a theoretical spectrum. The present invention improves the efficiency of optical modeling to obtain a theoretical spectrum.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement technology, and in particular to an optical characteristic modeling method and device, and an optical parameter measurement method. Background Art

[0002] As the semiconductor industry continues to advance toward deep submicron technology nodes, the line width of integrated circuits continues to shrink, and the design of integrated circuit device media becomes more complex. Therefore, only through strict process control can we obtain fully functional circuits and high-speed devices.

[0003] Optical critical dimension measurement technology is an important part of the current advanced process control of semiconductor manufacturing, with the advantages of fast speed, low cost and non-destructiveness. Fast and accurate optical property modeling and calculation method is one of the core elements of optical critical dimension measurement. Among the many optical property modeling and calculation methods, the Rigorous Coupled-Wave Analysis (RCWA) theory is widely used in the optical property modeling and calculation methods of periodic media due to its high modeling accuracy and wide application.

[0004] The commonly used calculation method for modeling optical properties is to perform Fourier series expansion on the dielectric constant of the material, the electromagnetic field in the incident area, the electromagnetic field in the sample area, and the electromagnetic field in the transmission area, and then substitute them into the Maxwell equations to form a coupled wave equation group of two orthogonal components of the electric field or magnetic field, and obtain the eigenvalue equation. Solve the eigenvalue equation to obtain the solution of the coupled wave equation group, and then obtain the Fourier coefficients of the two orthogonal components of the electric field or magnetic field. Then, according to the continuity condition of the electromagnetic field, the reflected electric field is obtained, and then the theoretical spectrum is obtained. The coupled wave equation group is as follows:

[0005] Among them, S y is the Fourier coefficient of the component of the electric field in the Y-axis direction, S x is the Fourier coefficient of the component of the electric field in the X-axis direction, K x , K y is a diagonal matrix and I is the identity matrix.

[0006] Solving the coupled wave equations can be achieved by solving the eigenvalue equation of the matrix PQ. The time to solve the eigenvalue equation of the matrix PQ is proportional to the cube of the dimensions of the matrix P and the matrix Q. The dimensions of the matrix P and the matrix Q in the prior art are 2(2M+1)(2N+1), so the time to solve the eigenvalue equation of the matrix PQ is proportional to 8(2M+1) 3 (2N+1) 3 , the solution efficiency is relatively low, resulting in low efficiency of optical modeling, which in turn affects the generation of subsequent theoretical spectra.

[0007] Therefore, the present invention provides an optical property modeling method and device, and an optical parameter measurement method, which improve the efficiency of optical modeling to obtain a theoretical spectrum. Summary of the invention

[0008] The present invention provides an optical property modeling method and device, and an optical parameter measurement method, which improve the efficiency of optical modeling to obtain a theoretical spectrum.

[0009] In a first aspect, the present invention provides a method for modeling optical properties, comprising: obtaining characteristic parameters of a periodic medium, and constructing a first coupled wave equation group based on the characteristic parameters and a rigorous coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about the Fourier coefficients of two orthogonal components of an electric field or the Fourier coefficients of two orthogonal components of a magnetic field; the periodic medium is symmetric about a light beam incident plane; obtaining a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, and constructing a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, wherein the second coupled wave equation group is a coupled wave equation group about the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; simplifying the second coupled wave equation group according to the symmetry of the periodic medium; solving the simplified second coupled wave equation group to obtain a theoretical spectrum.

[0010] The beneficial effect is that the present invention improves the efficiency of solving the second coupled wave equations by simplifying the second coupled wave equations according to the symmetry of the periodic medium, and further improves the efficiency of optical modeling to obtain a theoretical spectrum.

[0011] Optionally, obtaining a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field includes: obtaining a linear combination of two orthogonal components of at least two groups of electric fields, or obtaining a linear combination of two orthogonal components of at least two groups of magnetic fields.

[0012] Optionally, simplifying the second coupled wave equations according to the symmetry of the periodic medium includes: obtaining the symmetry of a linear combination of the Fourier coefficients of two orthogonal components of the electric field or the linear combination of the Fourier coefficients of two orthogonal components of the magnetic field; simplifying the second coupled wave equations based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field.

[0013] Optionally, obtaining the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field includes: obtaining the symmetric point (x', y') of any point (x, y) with respect to the incident plane of the light beam; obtaining the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at any point (x, y); the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at any point (x, y); obtaining the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at any point (x, y); the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at any point (x, y).

[0014] Alternatively, a linear combination of two orthogonal components of the two electric fields is obtained: aE x +bE y and cE x +dE y ; Correspondingly, the second coupled wave equations are:

[0015] in, S y (z) is the Fourier coefficient of the electric field component in the y direction, S x (z) is the Fourier coefficient of the component of the electric field in the x direction, a, b, c and d are real numbers; K x , K y is a diagonal matrix, and its diagonal elements are k xm is the wave vector component of each diffraction order in the x-axis direction, k yn is the wave vector component of each diffraction order in the y-axis direction; I is the unit matrix, and the element of the matrix E is ε m-p,n-q , ε mn is the Fourier coefficient of the dielectric constant, m and p are integers from -M to M, n and q are integers from -N to N, M and N are positive integers, M is the cutoff order of the series expansion in the X-axis direction, and N is the cutoff order of the series expansion in the Y-axis direction.

[0016] Further optionally, the solving the simplified second coupled wave equations to obtain the theoretical spectrum includes: obtaining a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field, obtaining the two orthogonal components of the electric field in the periodic medium reflection zone to obtain the theoretical spectrum.

[0017] In a second aspect, the present invention provides an optical parameter measurement method, comprising: establishing a spectral library, wherein the theoretical spectra in the spectral library are obtained by the optical property modeling method as described in any one of the first aspects; obtaining a measured spectrum of a sample to be tested, and searching the theoretical spectrum database for a theoretical spectrum matching the measured spectrum to determine the optical parameters of the sample to be tested.

[0018] In a third aspect, the present invention provides an optical property modeling device, configured to execute the optical property modeling method as described in any one of the first aspects, including: an acquisition module, a construction module and a calculation module; the acquisition module includes a first acquisition unit and a second acquisition unit, the construction module includes a first construction unit and a second construction unit, and the calculation module includes a first calculation unit and a second calculation unit; the first acquisition unit is used to acquire characteristic parameters of a periodic medium, and the first construction unit constructs a first coupled wave equation group based on the characteristic parameters and a rigorous coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about the Fourier coefficients of two orthogonal components of an electric field or the Fourier coefficients of two orthogonal components of a magnetic field; the periodic The periodic medium is symmetric about the incident plane of the light beam; the second acquisition unit is used to acquire the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field; the second construction unit constructs a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, and the second coupled wave equation group is a coupled wave equation group of a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; the first calculation unit is used to simplify the second coupled wave equation group according to the symmetry of the periodic medium; the second calculation unit is used to solve the simplified second coupled wave equation group to obtain a theoretical spectrum.

[0019] Optionally, the second acquisition unit includes: a first component acquisition unit or a second component acquisition unit, the first component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of electric fields, and the second component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of magnetic fields.

[0020] Optionally, the first calculation unit includes a symmetry acquisition unit, which is used to acquire the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field. The first calculation unit simplifies the second coupled wave equations based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; the second calculation unit includes a coefficient acquisition unit, which is used to acquire the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; the second calculation unit obtains the two orthogonal components of the electric field in the periodic medium reflection zone based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the theoretical spectrum.

[0021] For the beneficial effects of the second to third aspects, reference may be made to the description of the first aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 A flow chart of an embodiment of an optical property modeling method provided by the present invention;

[0023] Figure 2 A top view of a periodic medium provided by the present invention;

[0024] Figure 3 A flow chart of an embodiment of an optical parameter measurement method provided by the present invention;

[0025] Figure 4 A schematic diagram of an embodiment of an optical property modeling device provided by the present invention. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application. Among them, in the description of the embodiments of the present application, the terms used in the following embodiments are only for the purpose of describing specific embodiments, and are not intended to be used as limitations on the present application. As used in the specification and the appended claims of the present application, the singular expressions "a kind", "the", "above", "the" and "this" are intended to also include expressions such as "one or more", unless there is a clear contrary indication in the context. It should also be understood that in the following embodiments of the present application, "at least one", "one or more" refer to one or more (including two). The term "and / or" is used to describe the association relationship of associated objects, indicating that three relationships can exist; for example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone, where A and B can be singular or plural. The character " / " generally indicates that the associated objects before and after are in a kind of "or" relationship.

[0027] References to "one embodiment" or "some embodiments" etc. described in this specification mean that one or more embodiments of the present application include specific features, structures or characteristics described in conjunction with the embodiment. Thus, the statements "in one embodiment", "in some embodiments", "in some other embodiments", "in some other embodiments", etc. that appear in different places in this specification do not necessarily refer to the same embodiment, but mean "one or more but not all embodiments", unless otherwise specifically emphasized in other ways. The terms "including", "comprising", "having" and their variations all mean "including but not limited to", unless otherwise specifically emphasized in other ways. The term "connection" includes direct connection and indirect connection, unless otherwise specified. "First" and "second" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated.

[0028] In the embodiments of the present application, the words "exemplarily" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "exemplarily" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplarily" or "for example" is intended to present related concepts in a specific way.

[0029] In order to improve the efficiency of optical property modeling, the present invention provides an optical property modeling method, the process of which is as follows: Figure 1 As shown, the steps include:

[0030] S101, acquiring characteristic parameters of a periodic medium, wherein the periodic medium is symmetrical about a light beam incident plane. Exemplarily, incident light is incident on a surface of the periodic medium, and a reflection spectrum signal is measured, i.e., the periodic medium is disposed in an electric field and / or a magnetic field, and the characteristic parameters of the periodic medium include structural parameters and a period.

[0031] S102, constructing a first coupled wave equation group based on the characteristic parameters and the rigorous coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field. Exemplarily, the two orthogonal components of the electric field, the two orthogonal components of the magnetic field, and the dielectric coefficient are subjected to Fourier series expansion. The obtained Fourier series is substituted into the Maxwell equations to obtain a coupled wave equation group about the Fourier coefficients of the two orthogonal components of the electric field, or a coupled wave equation group about the Fourier coefficients of the two orthogonal components of the magnetic field, that is, the first coupled wave equation group.

[0032] S103, obtaining a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, and constructing a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, wherein the second coupled wave equation group is a coupled wave equation group of a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field.

[0033] S104, simplifying the second coupled wave equations according to the symmetry of the periodic medium. Exemplarily, when the periodic medium is symmetric about the beam incident plane, the obtained linear combination of the Fourier coefficients of the two orthogonal components of the electric field or magnetic field is also symmetric about the beam incident plane. Specifically, for any point (x, y) with respect to the symmetric point (x', y') of the beam incident plane, the linear combination of the Fourier series of the components of the electric field in the X-axis direction and the components in the Y-axis direction at the (x, y) coordinate point is 1 times or -1 times the linear combination of the Fourier series of the components in the X-axis direction and the components in the Y-axis direction at the symmetric point (x', y'); the linear combination of the Fourier coefficients of the components in the X-axis direction and the components in the Y-axis direction of the magnetic field at the (x, y) coordinate point is 1 times or -1 times the linear combination of the Fourier coefficients of the components in the X-axis direction and the components in the Y-axis direction at the symmetric point (x', y'). Then, the second coupled wave equations are simplified according to the symmetry to improve the efficiency of optical property modeling.

[0034] S105, solving the simplified second coupled wave equations to obtain a theoretical spectrum.

[0035] After solving the simplified second coupled wave equations, a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field is obtained, and the linear combination is further solved and calculated to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field. Exemplarily, based on the continuity condition of the electromagnetic field and the obtained Fourier coefficients, the two orthogonal components of the electric field in the reflection area are solved, and then the theoretical spectrum is obtained. The reflection area is the propagation area of ​​the incident light after being reflected on the surface of the sample to be tested.

[0036] In a possible embodiment, obtaining a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field includes: obtaining a linear combination of two orthogonal components of at least two groups of electric fields, or obtaining a linear combination of two orthogonal components of at least two groups of magnetic fields.

[0037] In another possible embodiment, simplifying the second coupled wave equations according to the symmetry of the periodic medium includes: obtaining the symmetry of a linear combination of the Fourier coefficients of two orthogonal components of the electric field or the linear combination of the Fourier coefficients of two orthogonal components of the magnetic field; and simplifying the second coupled wave equations based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field.

[0038] In another possible embodiment, obtaining the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field includes: obtaining the symmetric point (x', y') of any point (x, y) with respect to the incident plane of the light beam; obtaining the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at any point (x, y); the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at any point (x, y); obtaining the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at any point (x, y); the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at any point (x, y).

[0039] In one possible embodiment, a linear combination of two orthogonal components of two sets of electric fields is obtained: aE x +bE y and cE x +dE y ; Correspondingly, the second coupled wave equations are:

[0040] in, S y (z) is the Fourier coefficient of the electric field component in the y direction, S x (z) is the Fourier coefficient of the component of the electric field in the x direction, a, b, c and d are real numbers; K x , K y is a diagonal matrix, and its diagonal elements are k xm is the wave vector component of each diffraction order in the x-axis direction, k yn is the wave vector component of each diffraction order in the y-axis direction; I is the unit matrix, and the element of the matrix E is ε m-p,n-q , ε mn is the Fourier coefficient of the dielectric constant, m and p are integers from -M to M, n and q are integers from -N to N, M and N are positive integers, M is the cutoff order of the series expansion in the X-axis direction, and N is the cutoff order of the series expansion in the Y-axis direction.

[0041] In a possible embodiment, solving the simplified second coupled wave equations to obtain a theoretical spectrum includes: obtaining a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field, obtaining the two orthogonal components of the electric field in the periodic medium reflection zone to obtain the theoretical spectrum.

[0042] In the above embodiment, based on the sample model and the rigorous coupled wave analysis method, a coupled wave equation group is constructed; wherein the coupled wave equation group solves a linear combination of the Fourier coefficients of two orthogonal components of the electric field or a linear combination of the Fourier coefficients of two orthogonal components of the magnetic field. In the case where the periodic medium is symmetric about the incident plane, the coupled wave equation group is simplified, the matrix dimension of the eigenvalue equation is reduced, the efficiency of solving the eigenvalue equation is improved, and the calculation efficiency of the theoretical spectrum is improved.

[0043] In order to further explain the optical property modeling method mentioned in the above embodiment, an example is given here. For example, a rectangular coordinate system is established, such as Figure 2 As shown, the area in the solid-line frame represents the periodic space of the periodic medium, and the black area in the solid-line frame represents the model to be tested. The directions of the X-axis and the Y-axis in the rectangular coordinate system are as follows: Figure 2 As shown, the Z-axis direction in the rectangular coordinate system is perpendicular to the horizontal plane formed by the X-axis and the Y-axis ( Figure 2 The period of the periodic medium in the X-axis direction is ΛX , the period of the periodic medium in the Y-axis direction is Λ y Then the electric field at any position is The two orthogonal components of the electric field are E x 、E y , the two orthogonal components of the electric field E x 、E y Perform Fourier series expansion and we get Among them, S x,mn YesE x The Fourier coefficient, S y,mn YesE y The Fourier coefficients, k xm is the wave vector component of each diffraction order in the X-axis direction, k yn is the wave vector component of each diffraction order in the Y-axis direction, and in, λ0 is the wavelength, n1 is the refractive index of the incident region, Λ x ,Λ y are the periods of the periodic medium in the X-axis and Y-axis directions respectively, θ is the incident angle, and φ is the azimuth angle, that is, the angle formed by the incident plane of the light beam and the XOZ plane.

[0044] The magnetic field at any location is The two orthogonal components of the magnetic field are H x , H y , the two orthogonal components of the magnetic field H x , H y Perform Fourier series expansion and we get Among them, U x,mn Yes H x The Fourier coefficients, U y,mn Yes H y The Fourier coefficients of .

[0045] Expand the dielectric coefficient by Fourier series and get

[0046] Based on the characteristic parameters and the rigorous coupled wave analysis method, a first coupled wave equation group is constructed, that is, the Fourier series of the dielectric coefficient, the Fourier series of the two orthogonal components of the electric field, and the Fourier series of the two orthogonal components of the magnetic field are substituted into the Maxwell equations to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field, that is, the first coupled wave equation group, which is specifically: Among them, S y is the Fourier coefficient of the component of the electric field in the Y-axis direction, S xis the Fourier coefficient of the component of the electric field in the X-axis direction, K x , K y is a diagonal matrix, and its diagonal elements are I is the identity matrix, and the elements of matrix E are ε m-p,n-q , ε mn is the Fourier coefficient of the dielectric constant, m and p are integers from -M to M, n and q are integers from -N to N, M and N are positive integers, M is the cutoff order of the series expansion in the X-axis direction, and N is the cutoff order of the series expansion in the Y-axis direction.

[0047] The linear combination of the two orthogonal components of the electric field is aE x +bE y ,cE x +dE y , S y is the Fourier coefficient of the component of the electric field in the Y-axis direction, S x is the Fourier coefficient of the component of the electric field in the x-axis direction, a, b, c and d are real numbers; the linear combination of the two orthogonal components of the magnetic field is aH x +bH y , cH x +dH y , H y is the Fourier coefficient of the component of the magnetic field in the Y-axis direction, H x is the Fourier coefficient of the component of the magnetic field in the X-axis direction, and a, b, c and d are real numbers. Based on the first coupled wave equations, a coupled wave equation of a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field is constructed, i.e., the second coupled wave equations. Taking a=b=c=1, d=-1 as an example, we get the second coupled wave equations: In order to simplify the description, the symbol S is introduced. + =S y (z)+S x (z),S - =S y (z)-S x (z),U + =U y (z)+U x (z),U - =U y (z)-U x (z), we get This is further explained by taking an example of a light beam with an arbitrary incident angle, an azimuth angle of 45 degrees and a polarization angle of 0 degrees irradiating the surface of the sample model, wherein the azimuth angle is the angle formed by the incident plane of the light beam and the XOZ plane, and the polarization angle is the angle formed by the electric field vector and the incident plane of the light beam.

[0048] The sample model is a cubic column, and the periodic medium formed on the surface of the sample model has equal periods in the X-axis direction and the Y-axis direction, such as Figure 2 As shown, the area within the solid line frame represents the periodic space of the periodic medium, and the black area within the solid line frame represents the model to be tested, so the periodic medium in this embodiment is symmetrical about the incident plane of the light beam. Based on the incident conditions and periodic medium provided in this embodiment, the electromagnetic field formed on the surface of the sample model has the following symmetry about the incident plane of the light beam: the electric field component E in the X-axis direction at the position (x, y) x (x,y) is equal to the electric field component E in the Y-axis direction at the position (y,x) y (y,x); The magnetic field component H in the X-axis direction at the position (x,y) x (x, y) is equal to the magnetic field component H in the Y-axis direction at the position (y, x) y The negative of (y,x).

[0049] Therefore, the linear combination of the two orthogonal components of the electromagnetic field is also symmetrical about the incident plane. In this embodiment, a=b=c=1, d=-1, that is, the sum and difference of the two orthogonal components of the electromagnetic field are also symmetrical about the incident plane. Specifically, the sum of the X component and the Y component of the electric field at the position (x, y) is equal to the sum of the X component and the Y component of the electric field at the position (y, x), that is, E x (x,y)+E y (x,y)=E x (y,x)+E y (y,x), the difference between the Y component and the X component of the electric field at position (x,y) is equal to the negative of the difference between the Y component and the X component of the electric field at position (y,x), that is, E x (x,y)-E y (x,y)=-(E x (y,x)-E y (y,x)); the sum of the X component and the Y component of the magnetic field at the position (x, y) is equal to the negative of the sum of the X component and the Y component of the magnetic field at the position (y, x), that is, H x (x,y)+H y (x,y)=-(H x (y,x)+H y (y,x)), the difference between the Y component and the X component of the magnetic field at position (x, y) is equal to the difference between the Y component and the X component of the magnetic field at position (y, x), that is, H x(x,y)-H y (x,y)=H x (y,x)-H y (y,x).

[0050] Therefore, the Fourier coefficients corresponding to the electric field and magnetic field also have a corresponding relationship, that is, the (m, n) order pair of the Fourier coefficients of the sum of the two orthogonal components of the electric field and the (n, m) order pair of the Fourier coefficients of the sum of the two orthogonal components of the electric field are equal, that is, The (m, n) order pair of the Fourier coefficients of the difference of the two orthogonal components of the magnetic field and the (n, m) order pair of the Fourier coefficients of the difference of the two orthogonal components of the magnetic field are equal, that is, The (m, n) order pair of the Fourier coefficients of the difference of the two orthogonal components of the electric field and the (n, m) order pair of the Fourier coefficients of the difference of the two orthogonal components of the electric field are opposite numbers, that is, The (m, n) order pair of the Fourier coefficients of the sum of the two orthogonal components of the magnetic field and the (n, m) order pair of the Fourier coefficients of the sum of the two orthogonal components of the magnetic field are equal, that is,

[0051] The treatment scheme for irradiating the sample model surface with a beam of arbitrary incident angle, azimuth angle of 45 degrees and polarization angle of 90 degrees is similar. And the case of arbitrary polarization angle can be decomposed into a linear combination of 0 degrees and 90 degrees for solution.

[0052] Based on the symmetry of the Fourier coefficients of the linear combination of the X and Y components of the electromagnetic field, the coupled wave equations of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field, i.e., the second coupled wave equations, are simplified to obtain:

[0053] The above matrix E + The element of mn,pq , m≤n, p≤q, -M≤m≤M, -N≤n≤N, -M≤p≤M, -N≤q≤N, m, p, n, q are integers, M and N are both positive integers, The second coupled wave equations can be solved by solving the matrix The eigenvalue equation is implemented to solve the matrix The time of the eigenvalue equation is proportional to the matrix matrix The present invention uses the above calculation method to convert the matrix in the prior art and matrix The dimension of is reduced from 2(2M+1)(2N+1) to 2(2M+1)(N+1), so the matrix The time of the eigenvalue equation is proportional to 8(2M+1) 3 (2N+1) 3 Reduced to 8 (2M+1) 3 (N+1) 3 . So it greatly improves the solution matrix The calculation efficiency of the eigenvalue equation is improved, thereby improving the speed of solving the theoretical spectrum, and further improving the measurement efficiency of optical parameters. By solving the second coupled wave equation group, a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field is obtained, and then the linear combination is further solved and calculated to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field. Then, based on the continuity condition of the electromagnetic field, the two orthogonal components of the electric field in the reflection area are solved to obtain the theoretical spectrum. Compared with the prior art, the above embodiment reduces the matrix dimension of the eigenvalue equation, improves the efficiency of solving the eigenvalue equation, and improves the calculation efficiency of the theoretical spectrum.

[0054] Based on the optical property modeling method provided in any of the above embodiments, the present invention provides an optical parameter measurement method, the process of which is as follows: Figure 3 As shown, including:

[0055] S301, obtaining a theoretical spectrum obtained by the optical property modeling method described in any one of the above embodiments.

[0056] S302: establishing a theoretical spectrum database according to the theoretical spectrum.

[0057] S303, obtaining a measurement spectrum of the sample to be tested.

[0058] S304, searching the theoretical spectrum database for a theoretical spectrum matching the measured spectrum.

[0059] S305, determining the optical parameters of the sample to be measured according to the theoretical spectrum matching the measured spectrum.

[0060] In order to implement the optical property modeling method provided in the above embodiment, the present invention provides an optical property modeling device, such as Figure 4 As shown, the optical property modeling device includes an acquisition module 401 , a construction module 402 and a calculation module 403 .

[0061] The acquisition module 401 includes a first acquisition unit 4011 and a second acquisition unit 4012 , the construction module 402 includes a first construction unit 4021 and a second construction unit 4022 , and the calculation module 403 includes a first calculation unit 4031 and a second calculation unit 4032 .

[0062] The first acquisition unit 4011 is used to acquire characteristic parameters of the periodic medium, and the first construction unit 4021 constructs a first coupled wave equation group based on the characteristic parameters and the strict coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; the periodic medium is symmetrical about the incident plane of the light beam. The second acquisition unit 4012 is used to acquire the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, and the second construction unit 4022 constructs a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, wherein the second coupled wave equation group is a coupled wave equation group about the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; the first calculation unit 4031 is used to simplify the second coupled wave equation group according to the symmetry of the periodic medium; the second calculation unit 4032 is used to solve the simplified second coupled wave equation group to obtain a theoretical spectrum.

[0063] In a possible embodiment, the second acquisition unit includes: a first component acquisition unit or a second component acquisition unit, the first component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of electric fields, and the second component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of magnetic fields.

[0064] In another possible embodiment, the first calculation unit includes a symmetry acquisition unit, the symmetry acquisition unit is used to acquire the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field, and the first calculation unit simplifies the second coupled wave equations based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field. The second calculation unit includes a coefficient acquisition unit, the coefficient acquisition unit is used to acquire the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; the second calculation unit obtains the two orthogonal components of the electric field in the periodic medium reflection zone based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the theoretical spectrum.

[0065] All relevant contents of each step involved in the above method embodiment can be referred to the functional description of the corresponding unit module, and will not be repeated here.

[0066] The above is only a specific implementation of the embodiment of the present application, but the protection scope of the embodiment of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed in the embodiment of the present application should be included in the protection scope of the embodiment of the present application. Therefore, the protection scope of the embodiment of the present application should be based on the protection scope of the claims.

Claims

1. An optical property modeling method, characterized in that: include: Acquire characteristic parameters of the periodic medium, and construct a first coupled wave equation group based on the characteristic parameters and a rigorous coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about Fourier coefficients of two orthogonal components of an electric field or Fourier coefficients of two orthogonal components of a magnetic field; The periodic medium is symmetric about the incident plane of the light beam; Acquire a linear combination of two orthogonal components of the electric field or two orthogonal components of the magnetic field, and construct a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, wherein the second coupled wave equation group is a coupled wave equation group of a linear combination of Fourier coefficients of the two orthogonal components of the electric field or a linear combination of Fourier coefficients of the two orthogonal components of the magnetic field; simplifying the second coupled wave equations according to the symmetry of the periodic medium; The simplified second coupled wave equations are solved to obtain a theoretical spectrum.

2. The optical property modeling method according to claim 1, characterized in that: Obtaining a linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field includes: obtaining a linear combination of at least two groups of two orthogonal components of the electric field, or obtaining a linear combination of at least two groups of two orthogonal components of the magnetic field.

3. The optical property modeling method according to claim 1, characterized in that: The simplifying the second coupled wave equations according to the symmetry of the periodic medium comprises: Obtaining the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; Based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field, the second coupled wave equations are simplified.

4. The method for optical property modeling according to claim 3, characterized in that: Obtaining the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field comprises: Obtaining a symmetric point (x', y') of any point (x, y) with respect to the incident plane of the light beam; Obtaining a linear combination of Fourier coefficients of two orthogonal components of the electric field at any point (x, y); The linear combination of the Fourier coefficients of the two orthogonal components of the electric field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the electric field at any point (x, y); Obtaining a linear combination of Fourier coefficients of two orthogonal components of the magnetic field at any point (x, y); The linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at the symmetric point (x', y') is 1 or -1 times the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field at any point (x, y).

5. The method for optical property modeling according to claim 2, characterized in that: Get the linear combination of two orthogonal components of the two sets of electric fields: aE x +bE y and cE x +dE y ; Correspondingly, the second coupled wave equations are: in, S y (z) is the Fourier coefficient of the electric field component in the y direction, S x (z) is the Fourier coefficient of the component of the electric field in the x direction, a, b, c and d are real numbers; K x , K y is a diagonal matrix, and its diagonal elements are k xm is the wave vector component of each diffraction order in the x direction, k yn is the wave vector component of each diffraction order in the y direction, λ0 is the wavelength; I is the identity matrix, and the elements of the matrix E are ε m-p,n-q , ε mn is the Fourier coefficient of the dielectric constant, m and p are integers from -M to M, n and q are integers from -N to N, M and N are positive integers, M is the cutoff order of the series expansion in the X-axis direction, and N is the cutoff order of the series expansion in the Y-axis direction.

6. The optical property modeling method according to any one of claims 1 to 5, characterized in that: The step of solving the simplified second coupled wave equations to obtain a theoretical spectrum includes: Obtaining a linear combination of the Fourier coefficients of the two orthogonal components of the electric field or a linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; Based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field, the two orthogonal components of the electric field in the periodic medium reflection area are obtained to obtain a theoretical spectrum.

7. An optical parameter measurement method, characterized in that: include: Establishing a spectral library, wherein the theoretical spectra in the spectral library are obtained by the optical property modeling method according to any one of claims 1 to 6; A measurement spectrum of the sample to be tested is obtained, and a theoretical spectrum matching the measurement spectrum is searched in the theoretical spectrum database to determine the optical parameters of the sample to be tested.

8. An optical property modeling device, characterized in that: The optical property modeling method according to any one of claims 1 to 6 is configured to be executed, comprising: an acquisition module, a construction module and a calculation module; The acquisition module includes a first acquisition unit and a second acquisition unit, the construction module includes a first construction unit and a second construction unit, and the calculation module includes a first calculation unit and a second calculation unit; The first acquisition unit is used to acquire characteristic parameters of the periodic medium, and the first construction unit constructs a first coupled wave equation group based on the characteristic parameters and a rigorous coupled wave analysis method, wherein the first coupled wave equation group is a coupled wave equation group about the Fourier coefficients of two orthogonal components of the electric field or the Fourier coefficients of two orthogonal components of the magnetic field; the periodic medium is symmetric about the incident plane of the light beam; The second acquisition unit is used to acquire a linear combination of two orthogonal components of the electric field or two orthogonal components of the magnetic field, and the second construction unit constructs a second coupled wave equation group based on the first coupled wave equation group and the linear combination of the two orthogonal components of the electric field or the two orthogonal components of the magnetic field, wherein the second coupled wave equation group is a coupled wave equation group of a linear combination of Fourier coefficients of two orthogonal components of the electric field or a linear combination of Fourier coefficients of two orthogonal components of the magnetic field; The first calculation unit is used to simplify the second coupled wave equations according to the symmetry of the periodic medium; The second calculation unit is used to solve the simplified second coupled wave equations to obtain a theoretical spectrum.

9. The optical characteristic modeling device according to claim 8, characterized in that: The second acquisition unit includes: a first component acquisition unit or a second component acquisition unit, the first component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of electric fields, and the second component acquisition unit is used to acquire a linear combination of two orthogonal components of at least two groups of magnetic fields.

10. The optical characteristic modeling device according to claim 9, characterized in that: The first calculation unit includes a symmetry acquisition unit, the symmetry acquisition unit is used to acquire the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field, and the first calculation unit simplifies the second coupled wave equations based on the symmetry of the linear combination of the Fourier coefficients of the two orthogonal components of the electric field or the linear combination of the Fourier coefficients of the two orthogonal components of the magnetic field; The second calculation unit includes a coefficient acquisition unit, and the coefficient acquisition unit is used to acquire a linear combination of Fourier coefficients of two orthogonal components of the electric field or a linear combination of Fourier coefficients of two orthogonal components of the magnetic field to obtain the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field; The second calculation unit obtains two orthogonal components of the electric field of the periodic medium reflection area based on the continuity condition of the electromagnetic field and the Fourier coefficients of the two orthogonal components of the electric field or the Fourier coefficients of the two orthogonal components of the magnetic field to obtain a theoretical spectrum.

Images